There is a need for more efficient arithmetic circuitry and methods for improving the speed of logarithmic computations in a computer. Present logarithm computing systems typically utilize a hardware fixed point processor with an algorithm based on a CORDIC (COordinate Rotation DIgital Computer) computing technique, such as the logarithm computing system described by Walther in A Unified Algorithm For Elementary Functions, Spring Joint Computer Conference, 1971, or in the method of Tien Chi Chen in U.S. Pat. No. 3,631,230. Both the CORDIC and Chen's system require hardware implementation for efficiency. A system that could be implemented entirely in software is needed to provide an alternative of conserving hardware costs and improving physical space requirements.